Find the area of a regular octagon with apothem K and side of 10

Solution:

Given a regular octagon with side 10 units and apothem as K

We know that area of the octagon is given as:

A = (P*a)/2 where P is the perimeter of the octagon and a is the apothem.

An octagon has 8 sides, our side length is 10

The perimeter is the sum of all sides of the polygon

We get perimeter as 10 × 8 = 80 perimeter is the sum of all sides of the polygon

So, (80*k)/2 = 40k.

Thus, 40k is the area of the octagon

Find the area of a regular octagon with apothem K and side of 10

Summary:

The area of a regular octagon with apothem K and side of 10 is 40K.